# Entropy bound of horizons for accelerating, rotating and charged Plebanski–Demianski black hole

## Abstract

We first review the accelerating, rotating and charged Plebanski–Demianski (PD) black hole, which includes the Kerr–Newman rotating black hole and the Taub-NUT spacetime. The main feature of this black hole is that it has 4 horizons like event horizon, Cauchy horizon and two accelerating horizons. In the non-extremal case, the surface area, entropy, surface gravity, temperature, angular velocity, Komar energy and irreducible mass on the event horizon and Cauchy horizon are presented for PD black hole. The entropy product, temperature product, Komar energy product and irreducible mass product have been found for event horizon and Cauchy horizon. Also their sums are found for both horizons. All these relations are dependent on the mass of the PD black hole and other parameters. So all the products are not universal for PD black hole. The entropy and area bounds for two horizons have been investigated. Also we found the Christodoulou–Ruffini mass for extremal PD black hole. Finally, using first law of thermodynamics, we also found the Smarr relation for PD black hole.

- Authors:

- Publication Date:

- OSTI Identifier:
- 22617384

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics; Journal Volume: 372; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BLACK HOLES; ENTROPY; GRAVITATION; SPACE-TIME; THERMODYNAMICS

### Citation Formats

```
Debnath, Ujjal, E-mail: ujjaldebnath@yahoo.com.
```*Entropy bound of horizons for accelerating, rotating and charged Plebanski–Demianski black hole*. United States: N. p., 2016.
Web. doi:10.1016/J.AOP.2016.06.014.

```
Debnath, Ujjal, E-mail: ujjaldebnath@yahoo.com.
```*Entropy bound of horizons for accelerating, rotating and charged Plebanski–Demianski black hole*. United States. doi:10.1016/J.AOP.2016.06.014.

```
Debnath, Ujjal, E-mail: ujjaldebnath@yahoo.com. Thu .
"Entropy bound of horizons for accelerating, rotating and charged Plebanski–Demianski black hole". United States. doi:10.1016/J.AOP.2016.06.014.
```

```
@article{osti_22617384,
```

title = {Entropy bound of horizons for accelerating, rotating and charged Plebanski–Demianski black hole},

author = {Debnath, Ujjal, E-mail: ujjaldebnath@yahoo.com},

abstractNote = {We first review the accelerating, rotating and charged Plebanski–Demianski (PD) black hole, which includes the Kerr–Newman rotating black hole and the Taub-NUT spacetime. The main feature of this black hole is that it has 4 horizons like event horizon, Cauchy horizon and two accelerating horizons. In the non-extremal case, the surface area, entropy, surface gravity, temperature, angular velocity, Komar energy and irreducible mass on the event horizon and Cauchy horizon are presented for PD black hole. The entropy product, temperature product, Komar energy product and irreducible mass product have been found for event horizon and Cauchy horizon. Also their sums are found for both horizons. All these relations are dependent on the mass of the PD black hole and other parameters. So all the products are not universal for PD black hole. The entropy and area bounds for two horizons have been investigated. Also we found the Christodoulou–Ruffini mass for extremal PD black hole. Finally, using first law of thermodynamics, we also found the Smarr relation for PD black hole.},

doi = {10.1016/J.AOP.2016.06.014},

journal = {Annals of Physics},

number = ,

volume = 372,

place = {United States},

year = {Thu Sep 15 00:00:00 EDT 2016},

month = {Thu Sep 15 00:00:00 EDT 2016}

}