Positivity of holographic energy
Piotr T. Chruściel, Raphaela Wutte
TLDR
This paper proves the positivity of weighted holographic energy for 4D spacetimes with negative cosmological constant under specific boundary conditions.
Key contributions
- Proves positivity of a weighted holographic energy.
- Applies to four-dimensional spacetimes with negative cosmological constant.
- Requires a conformally static conformal boundary at infinity.
- Boundary sections must be spherical or toroidal with compatible spin structure.
Why it matters
Proving the positivity of holographic energy is crucial for understanding gravitational energy in anti-de Sitter (AdS) spacetimes. This result contributes to the theoretical foundations of the AdS/CFT correspondence, ensuring well-behaved energy definitions under specific boundary conditions.
Original Abstract
We prove positivity of a weighted holographic energy for four-dimensional spacetimes with negative cosmological constant whose conformal boundary at infinity is conformally static and admits either spherical sections, or toroidal sections with compatible spin structure.
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