Re-derivation of the constant-density star in isotropic coordinates produces a transparent metric and highlights under-appreciated special cases including pressure gravitating alone and naked singularities.
Gravitational vacuum polarization III: Energy conditions in the (1+1) Schwarzschild spacetime
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abstract
Building on a pair of earlier papers, I investigate the various point-wise and averaged energy conditions for the quantum stress-energy tensor corresponding to a conformally-coupled massless scalar field in the in the (1+1)-dimensional Schwarzschild spacetime. Because the stress-energy tensors are analytically known, I can get exact results for the Hartle--Hawking, Boulware, and Unruh vacua. This exactly solvable model serves as a useful sanity check on my (3+1)-dimensional investigations wherein I had to resort to a mixture of analytic approximations and numerical techniques. Key results in (1+1) dimensions are: (1) NEC is satisfied outside the event horizon for the Hartle--Hawking vacuum, and violated for the Boulware and Unruh vacua. (2) DEC is violated everywhere in the spacetime (for any quantum state, not just the standard vacuum states).
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gr-qc 1years
2026 1verdicts
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Revisiting Schwarzschild's constant density star in isotropic coordinates
Re-derivation of the constant-density star in isotropic coordinates produces a transparent metric and highlights under-appreciated special cases including pressure gravitating alone and naked singularities.