Pith Number

pith:EKVSX2IB

pith:2026:EKVSX2IBILI5KED67TEDXRM4P7

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Derivation of the Smarr formula from the Komar charge in Einstein-nonlinear electrodynamics theories and applications to regular black holes

Gabriele Barbagallo, Tom\'as Ort\'in

The generalized Komar charge for Einstein-NLED theories yields a Smarr formula that includes the coupling constant contribution.

arxiv:2605.02813 v2 · 2026-05-04 · gr-qc · hep-th

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Claims

C1strongest claim

We construct the generalized Komar charge of generic, non-linear theories of electrodynamics (NLED) in 4 dimensions coupled to Einstein gravity. ... We use this charge to derive a Smarr formula for asymptotically-flat black-hole and soliton solutions of these theories that includes the contribution of the coupling constant.

C2weakest assumption

The contribution of the dimensionful coupling constant present in all these theories is obtained by promoting it to a dynamical field which is forced to be constant on-shell by a Lagrange multiplier.

C3one line summary

A generalized Komar charge constructed via Lagrange multiplier promotion of the coupling constant yields a Smarr formula including that constant's contribution for asymptotically flat black hole and soliton solutions in Einstein-NLED theories, with application to the Bardeen regular black hole.

Formal links

3 machine-checked theorem links

Receipt and verification

First computed	2026-06-12T01:09:28.484198Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

22ab2be90142d1d5107efcc83bc59c7fd5bb461c7795d6d586bb819403698448

Aliases

arxiv: 2605.02813 · arxiv_version: 2605.02813v2 · doi: 10.48550/arxiv.2605.02813 · pith_short_12: EKVSX2IBILI5 · pith_short_16: EKVSX2IBILI5KED6 · pith_short_8: EKVSX2IB

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/EKVSX2IBILI5KED67TEDXRM4P7 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 22ab2be90142d1d5107efcc83bc59c7fd5bb461c7795d6d586bb819403698448

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "59536e04c9ad104e0f7b71ccc901445b94fe43220c63589125c0d032fc4ba12e",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-05-04T16:49:43Z",
    "title_canon_sha256": "65e4dc82d9258013ee6d72c11796e72b6e10ea596c7b997d3012698b3b844002"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.02813",
    "kind": "arxiv",
    "version": 2
  }
}