Research Article Cardy-Verlinde Formula of Noncommutative Schwarzschild Black Hole G. Abbas Department of Mathematics, COMSATS Institute of Information Technology, Sahiwal 57000, Pakistan Correspondence should be addressed to G. Abbas; abbasg91@yahoo.com Received 19 November 2013; Revised 3 February 2014; Accepted 13 February 2014; Published 18 March 2014 Academic Editor: George Siopsis Copyright © 2014 G. Abbas. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Te publication of this article was funded by SCOAP 3 . Few years ago, Setare (2006) has investigated the Cardy-Verlinde formula of noncommutative black hole obtained by nonco- mmutativity of coordinates. In this paper, we apply the same procedure to a noncommutative black hole obtained by the coordinate coherent approach. Te Cardy-Verlinde formula is entropy formula of conformal feld theory in an arbitrary dimension. It relates the entropy of conformal feld theory to its total energy and Casimir energy. In this paper, we have calculated the total energy and Casimir energy of noncommutative Schwarzschild black hole and have shown that entropy of noncommutative Schwarzschild black hole horizon can be expressed in terms of Cardy-Verlinde formula. 1. Introduction Verlinde [1] proved that the entropy of conformal feld theory in arbitrary dimension is related to its total energy and Casimir energy; this is known as generalized Verlinde formula (commonly termed as Cardy-Verlinde formula). Recently, it has been investigated that this formula holds well for Reissner-Nordstr¨ om de-Sitter black hole (BH) [2] and charged Kerr BH [3]. Birmingham and Mokhtari proved the validity of Birmingham and Mokhtari [4] proved the Verlinde formula for Taub-Bolt-Anti-de-Sitter BH. Setare and Jamil [5] discussed the Cardy-Verlinde formula for charged BTZ BH. Many authors [6–11] have proved the validity of Cardy- Verlinde for diferent BHs. Te purpose of this paper is to investigate the validity of Cardy-Verlinde entropy formula for NC Schwarzschild BH. In classical general relativity (GR), the curvature sin- gularity is such a point where physical description of the gravitational feld is impossible. Tis problem can be removed in GR by taking into account the quantum mechanical treatment to the standard formulation of GR. Motivated by such reasoning, some BH solutions in noncommutative (NC) feld theory have been derived. In these solutions, curvature singularity at origin is removed by de-Sitter core which is introduced due to NC nature of spacetime [12]. Ansoldi et al. [13] formulated the NC charged BHs solutions; this was extended to rotating noncommutative BHs case by Modesto and Nicolini [14]. Mann and Nicoloni [15] have discussed the cosmological production of NC BHs. Te frst NC version of wormholes solution was investigated by Nicolini and Spallucci [16]. Farook et al. [17] have investigated the higher dimensional wormhole solutions in NC theory of gravity. Motivated by such NC correction to BHs, Sharif and Abbas [18] studied the thin shell collapse in NC Reissner-Nordstr¨ om geometry. Banerjee and Gangopadhyay [19] derived the Komar energy and Sammar formula for NC Schwarzschild BH. Motivated by the recent development in NC theory of gravity, we have proved that the entropy of NC Schwarzschild BH horizon can be expressed in terms of Cardy-Verlinde formula. For this purpose, we have used the Setare and Jamil method [5]. Te plan of the paper is as follows. In Section 2, we briefy discussed the the thermodynamical relations of NC Schwarzschild BH and Cardy-Verlinde formula and proved that entropy of noncommutative Schwarzschild BH horizon can be expressed in terms of Cardy-Verlinde formula. Section 3 is devoted to the concluded remarks of the work done. Hindawi Publishing Corporation Advances in High Energy Physics Volume 2014, Article ID 306256, 4 pages http://dx.doi.org/10.1155/2014/306256