Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas | Paper Citation Record

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This paper cites In the nonrelativistic limit, using the representation η(Λ), the hot spiral is rejected at inﬁnity and only the cold spiral remains.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas In the nonrelativistic limit, using the representation η(Λ), the hot spiral is rejected at inﬁnity and only the cold spiral remains

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This paper cites (56), we get P (r) ϵkin(r)→ 1.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas (56), we get P (r) ϵkin(r)→ 1

Reference 2

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This paper cites (49)-(51) we can write ϵkin(r) =n(r)mc2F(b(r)), ϵ (r) =n(r)mc2 [1 +F(b(r))], (54) where we have introduced the function [15]: F(z) = K1(z) K2(z) + 3 z− 1.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas (49)-(51) we can write ϵkin(r) =n(r)mc2F(b(r)), ϵ (r) =n(r)mc2 [1 +F(b(r))], (54) where we have introduced the function [15]: F(z) = K1(z) K2(z) + 3 z− 1

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Unresolved cited work

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Observation 0de18e53-66e6-4241-9e42-332acfc697c3 · outbound

This paper cites (64) For a given value of α and T0 one can solve Eqs.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas (64) For a given value of α and T0 one can solve Eqs

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This paper cites We can also directly substitute the relation (67) into the Juttner equations (49)-(52).

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas We can also directly substitute the relation (67) into the Juttner equations (49)-(52)

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas constant

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Unresolved cited work

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Observation 8f7d7470-e446-4566-9bd3-bc368b573c84 · outbound

This paper cites Horwitz, J.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Horwitz, J

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This paper cites avalanche-type catastrophic contraction of the system.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas avalanche-type catastrophic contraction of the system

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Sorkin, R.M

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Observation 5c67cb6d-dea4-41da-86f6-3ff432e756fb · outbound

This paper cites cold spiral.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas cold spiral

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Observation c0f4335e-d943-4ed2-b095-19fa81b4cef2 · outbound

This paper cites cold” spiral at negative energies. We now consider the relativistic parts of the caloric curves. In that case, a “hot.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas cold” spiral at negative energies. We now consider the relativistic parts of the caloric curves. In that case, a “hot

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This paper cites To solve this maximization problem, we proceed in two steps.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas To solve this maximization problem, we proceed in two steps

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This paper cites To solve this maximization problem, we proceed in two steps.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas To solve this maximization problem, we proceed in two steps

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Chavanis, preprint (Paper I)

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Tolman, Phys

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Cocke, Ann

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Horwitz, J

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Unresolved cited work

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Unresolved cited work

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Unresolved cited work

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Unresolved cited work

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Prabhu, J.S

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Ipser, Astrophys

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Oppenheimer, G.M

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Bilic, R.D

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Chavanis, Astron

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Gao, Phys

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Green, J.S

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Klein, Rev

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Caloric curves of self-gravitating fermions in general relativity

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas King, Astron

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Antonov, Vest

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Zel’dovich, M.A

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Larson, Mon

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Hachisu, Y

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Lynden-Bell, P.P

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Cohn, Astrophys

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Inagaki, D

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Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Sugimoto, E

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Resolution: unresolved; no resolver link, observed 2026-08-14T10:42:00.885620Z

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Observation 2c0492ea-ee5c-49cc-9a8f-3e2a5b3cf14a · outbound

This paper cites Heggie, N.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Heggie, N

Reference 65

Resolution: unresolved; no resolver link, observed 2026-08-14T10:42:00.889227Z

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Observation 5111fa7e-1ddc-483d-8805-4df7826613c8 · outbound

This paper cites Doremus, M.R.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Doremus, M.R

Reference 66

Resolution: unresolved; no resolver link, observed 2026-08-14T10:42:00.892803Z

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Observation aa73729e-1481-4338-a49c-bdacadb969bf · outbound

This paper cites Doremus, M.R.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Doremus, M.R

Reference 67

Resolution: unresolved; no resolver link, observed 2026-08-14T10:42:00.896415Z

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Observation 08c72547-edb0-46d5-978f-e712382fd17f · outbound

This paper cites Gillon, M.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Gillon, M

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Resolution: unresolved; no resolver link, observed 2026-08-14T10:42:00.900374Z

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Observation 924f3431-af1c-4498-8d13-ade19aa57577 · outbound

This paper cites Sygnet, G.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Sygnet, G

Reference 69

Resolution: unresolved; no resolver link, observed 2026-08-14T10:42:00.904098Z

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Observation e0ed7112-3c10-4aa7-9203-9ecc3c17dbb2 · outbound

This paper cites Kandrup, J.F.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Kandrup, J.F

Reference 70

Resolution: unresolved; no resolver link, observed 2026-08-14T10:42:00.907705Z

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Observation 82196ede-64e5-42c0-9a17-251fc6638c51 · outbound

This paper cites Kandrup, Astrophys.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Kandrup, Astrophys

Reference 71

Resolution: unresolved; no resolver link, observed 2026-08-14T10:42:00.911158Z

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Observation 91c7d6ba-2d1f-4b24-93d9-3ce3d4801d45 · outbound

This paper cites Fackerell, Ph.D.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Fackerell, Ph.D

Reference 72

Resolution: unresolved; no resolver link, observed 2026-08-14T10:42:00.918199Z

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Observation 58395e2d-bcd1-47b1-afbf-29d5afaf7b34 · outbound

This paper cites Fackerell, Astrophys.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Fackerell, Astrophys

Reference 73

Resolution: unresolved; no resolver link, observed 2026-08-14T10:42:00.922736Z

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Observation 9c8fd5f2-1708-4808-a37b-72cec6788b30 · outbound

This paper cites Ipser, K.S.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Ipser, K.S

Reference 74

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:42:02.184097Z

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Observation 6cc5ff94-dae9-4f1d-b148-9d19bbb69402 · outbound

This paper cites Ipser, Astrophys.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Ipser, Astrophys

Reference 75

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:42:02.173434Z

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Observation 7da185f0-ac25-451e-90b5-8832b8333544 · outbound

This paper cites Ipser, Astrophys.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Ipser, Astrophys

Reference 76

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:42:02.162015Z

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Observation 0f2abafc-d122-46be-9837-729c7690b581 · outbound

This paper cites Fackerell, Astrophys.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Fackerell, Astrophys

Reference 77

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:42:02.150202Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 1e04d5de-2066-4786-98db-538e58f27cfa · outbound

This paper cites Sudbury, Mon.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Sudbury, Mon

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:42:02.138451Z

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Observation 1ea90028-9f2e-4d99-bd5d-f243fd8149e3 · outbound

This paper cites Suﬀern, E.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Suﬀern, E

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:42:02.126888Z

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Observation bfc21614-f41e-4006-ad56-ef9bad24ba18 · outbound

This paper cites Fackerell, K.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Fackerell, K

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:42:02.114315Z

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Observation c7340f8d-9ff7-4456-bbfe-2e17d6ad938e · outbound

This paper cites Meraﬁna, R.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Meraﬁna, R

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:42:02.100992Z

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Observation 470f8a91-18f5-4272-b72c-472096442859 · outbound

This paper cites Meraﬁna, R.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Meraﬁna, R

Reference 82

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:42:02.088647Z

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Observation 007a8063-3a31-440f-92a9-7fab538aa330 · outbound

This paper cites Meraﬁna, R.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Meraﬁna, R

Reference 83

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:42:02.076840Z

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Observation 5ade6fd8-ebec-4208-8521-7d64f23e650e · outbound

This paper cites Bisnovatyi-Kogan, M.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Bisnovatyi-Kogan, M

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:42:02.064764Z

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Observation 25c49bec-2f99-4733-af9a-a756c3baf8ee · outbound

This paper cites Bisnovatyi-Kogan, M.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Bisnovatyi-Kogan, M

Reference 85

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:42:02.052828Z

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Observation ab08a265-236d-47b5-b17e-d6eb9dcb228e · outbound

This paper cites Poincar´ e, Acta Math.7, 259 (1885).

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Poincar´ e, Acta Math.7, 259 (1885)

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Resolution: unresolved; no resolver link, observed 2026-08-14T10:42:00.976735Z

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Observation 8eb3b7a3-d61b-48e6-8941-f8bc4a996b38 · outbound

This paper cites Fackerell, J.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Fackerell, J

Reference 87

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:42:02.033103Z

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Observation 1e73065c-11a9-405b-89bd-866fa98b9005 · outbound

This paper cites Shapiro, S.A.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Shapiro, S.A

Reference 88

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:42:02.021324Z

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Observation 223ea85f-c245-430b-96e3-20623d216d34 · outbound

This paper cites Shapiro, S.A.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Shapiro, S.A

Reference 89

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:42:02.009609Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 335c2a6d-8f53-459d-b8e4-9bb6809305d5 · outbound

This paper cites Shapiro, S.A.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Shapiro, S.A

Reference 90

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:42:01.997590Z

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Observation 62cded89-6540-47db-b4b9-a3c11e25d936 · outbound

This paper cites Shapiro, S.A.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Shapiro, S.A

Reference 91

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:42:01.986346Z

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Observation 5a121890-9162-45a7-ba5f-8805b1dc5e53 · outbound

This paper cites Kochanek, S.L.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Kochanek, S.L

Reference 92

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:42:01.975194Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 5f8b797f-cee6-48fc-be6a-86e7e8ee83d6 · outbound

This paper cites Rasio, S.L.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Rasio, S.L

Reference 93

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:42:01.964535Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation c00d773c-2fcd-4344-905e-42953c940731 · outbound

This paper cites Shapiro, S.A.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Shapiro, S.A

Reference 94

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:42:01.952626Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 7cdfa34a-5002-44c3-821b-cb73c0d63573 · outbound

This paper cites Shapiro, S.A.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Shapiro, S.A

Reference 95

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:42:01.940982Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 11401184-ff3b-4415-b0c6-c8d2b25884b9 · outbound

This paper cites Shapiro, S.A.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Shapiro, S.A

Reference 96

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:42:01.928908Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation a9c421ba-c837-410f-a9d3-c85785bfa291 · outbound

This paper cites Hoyle, W.A.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Hoyle, W.A

Reference 97

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:42:01.916082Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation a57eb5f4-3db5-45a3-b589-f92f71c04a81 · outbound

This paper cites Hoyle, W.A.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Hoyle, W.A

Reference 98

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:42:01.904271Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 74598505-74f7-4ba2-99a0-694c739850d1 · outbound

This paper cites Hoyle, W.A.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Hoyle, W.A

Reference 99

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:42:01.890607Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 3a5d66f3-2d0b-456f-b177-2206ce5bd578 · outbound

This paper cites Zapolsky, Astrophys.

Statistical mechanics of self-gravitating systems in general relativity: II. The classical Boltzmann gas Zapolsky, Astrophys

Reference 100

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T10:42:01.878562Z

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