Warped vacuum energy by black holes

Abstract The belief still persists, at least for an important part of the community, that in general relativity the cosmological constant $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> must remain immaculate. However, Bianchi identities show that $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> could acquire local properties in the presence of matter, i.e., $$\Lambda \rightarrow \,\Lambda (x^\mu )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Λ</mml:mi> <mml:mo>→</mml:mo> <mml:mspace/> <mml:mi>Λ</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>x</mml:mi> <mml:mi>μ</mml:mi> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . In this paper we go even further, and we show that a non-uniform vacuum energy does not even require coexistence with any additional form of matter-energy, nor of any theory beyond general relativity, at least for extreme environments, such as the proximity of a black hole.

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