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Thermodynamic Products for Sen Black Hole

Parthapratim Pradhan
(
- West Bengal State U.
)

Mar 15, 2015

20 pages

Published in:

Eur.Phys.J.C 76 (2016) 3, 131,
Eur.Phys.J.C 81 (2021) 10, 896 (erratum)

Published: Mar 9, 2016
and
Published: Oct 11, 2021

e-Print:

1503.04514 [gr-qc]

DOI:

10.1140/epjc/s10052-016-3976-1,
10.1140/epjc/s10052-021-09699-0 (erratum)

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Abstract: (Springer)

We investigate the properties of inner and outer horizon thermodynamics of Sen black hole (BH) both in Einstein frame (EF) and string frame (SF). We also compute area (or entropy) product, area (or entropy) sum of the said BH in EF as well as SF. In the EF, we observe that the area (or entropy) product is universal, whereas area (or entropy) sum is not universal. On the other hand, in the SF, area (or entropy) product and area (or entropy) sum don’t have any universal behaviour because they all are depends on Arnowitt–Deser–Misner (ADM) mass parameter. We also verify that the first law is satisfied at the Cauchy horizon as well as event horizon (EH). In addition, we also compute other thermodynamic products and sums in the EF as well as in the SF. We further compute the Smarr mass formula and Christodoulou’s irreducible mass formula for Sen BH. Moreover, we compute the area bound and entropy bound for both the horizons. The upper area bound for EH is actually the Penrose like inequality, which is the first geometric inequality in BHs. Furthermore, we compute the central charges of the left and right moving sectors of the dual CFT in Sen/CFT correspondence using thermodynamic relations. These thermodynamic relations on the multi-horizons give us further understanding the microscopic nature of BH entropy (both interior and exterior).

Note:

Accepted for publication in EPJC

horizon: thermodynamics
entropy
Einstein
string
thermodynamical
mass formula
black hole: thermodynamics
universality
mass: gravitation
field theory: conformal

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