Abstract
Most of the important and powerful theorems in General Relativity such as singularity theorems and the theorems applied for null horizons depend strongly on the energy conditions. However, the energy conditions on which these theorems are based on, are beginning to look at less secure if one takes into accounts quantum effects which can violate these energy conditions. Even there are classical systems that can violate these energy conditions which would be problematic in validation of those theorems. In this article, we revisit to a class of such important theorems, the laws of black hole mechanics which are meant to be developed on null like killing horizons using null energy condition. Then we show some classical and quantum mechanical systems which violate null energy condition based on which the above theorem stands.
Highlights
General Relativity, one of the successful theory in modern physics which describes gravity successfully in terms of introducing the concepts of spacetime manifolds, is often considered to be tremendously complex theory when one is looking for solutions of Einstein equation Gμν = 8πG c4 Tμν (1)Left hand side of this equation comes from description of geometry of spacetime manifolds which by itself is complicated covariant tensor of rank 2 but it is at least universal function of spacetime geometry
We revisit to a class of such important theorems, the laws of black hole mechanics which are meant to be developed on null like killing horizons using null energy condition
Whether the oscillatory term leads to violations of Null energy condition (NEC) or not, depends on the normalization of the state; an example where this becomes apparent is the vacuum + 2 particles states, for which exactly half of the phase space covered by these states gives rise to NEC violations and the other half does not [36]
Summary
General Relativity, one of the successful theory in modern physics which describes gravity successfully in terms of introducing the concepts of spacetime manifolds, is often considered to be tremendously complex theory when one is looking for solutions of Einstein equation. Based on above one can have two choices of which first is to do special-case calculations, one for each conceivable matter action or second is develop general theorems based on some generic features which reasonably all stress-energy should satisfy. One such feature that most matter seems to share (found mostly through experiments) is that energy densities (almost) always seem to be positive. It has become clear that there are classical field theories [2] [3] that violate energy condition but compatible with all known experiments. This directly concludes that above theorems are weakly valid and any spacetime whose source stressenergy tensor violates null energy condition for them such theorems does not hold unless statements of the theorems are suitably corrected
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