Abstract
We study the properties of five-dimensional black objects by using the renormalized boundary stress tensor for locally asymptotically flat spacetimes. This provides a more refined form of the quasilocal formalism, which is useful for a holographic interpretation of asymptotically flat gravity. We apply this technique to examine the thermodynamic properties of black holes, black rings and black strings. The advantage of using this method is that we can go beyond the ‘thin ring’ approximation and compute the boundary stress tensor for any general (thin or fat) black ring solution. We argue that the boundary stress tensor encodes the necessary information to distinguish between black objects with different horizon topologies in the bulk. We also study in detail the susy black ring and clarify the relation between the asymptotic charges and the charges defined at the horizon. Furthermore, we obtain the balance condition for ‘thin’ dipole black rings.
Highlights
A remarkable development in theoretical physics was the discovery of a close relationship between the laws of thermodynamics and certain laws of black hole physics
In a very basic sense, gravitational entropy can be regarded as arising from the Gibbs– Duhem relation applied to the path-integral formulation of quantum gravity [1]
This relationship was first explored in the context of black holes by Gibbons and Hawking [2], who argued that the thermodynamical potential is equal to the Euclidean gravitational action multiplied by the temperature
Summary
A remarkable development in theoretical physics was the discovery of a close relationship between the laws of thermodynamics and certain laws of black hole physics. This yields a relationship between gravitational entropy and other relevant thermodynamic quantities, such as mass, angular momentum and other conserved charges This relationship was first explored in the context of black holes by Gibbons and Hawking [2], who argued that the thermodynamical potential is equal to the Euclidean gravitational action multiplied by the temperature. The integral is computed by using the saddle-point approximation When applying this method to the Schwarzschild black hole, the calculation is purely gravitational (no additional ‘matter’ fields are present) and the entropy is one-fourth of the horizon area. The conserved quantities can be constructed from this stress tensor via the algorithm of Brown and York [3] As an example, this method was applied in [13] to understand the thermodynamics of the dipole ring [14].
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