We focus on the energy content (including matter and fields) of the Møller energy-momentum complex in the framework of Einstein-Maxwell-Dilaton-Axion (EMDA) theory using teleparallel gravity. We perform the required calculations for some specific charged black hole models, and we find that total energy distributions associated with asymptotically flat black holes are proportional to the gravitational mass. On the other hand, we see that the energy of the asymptotically nonflat black holes diverge in a limiting case.

There are many interesting theories aiming to investigate gravitational effects: general relativity and teleparallel gravity. In these theories, calculating the energy-momentum distribution is an old and interesting problem. One can construct a teleparallel equivalent of the general relativity by assuming that curvature and torsion give the equivalent descriptions of the gravitational interactions.

In order to avoid the singularities in the general relativity and to give a general definition of energy momentum, Møller obtained a new expression by using the teleparallel gravity [

The study carried out by Vargas [

This paper is organized as follows. In the next section we introduce Møller energy-momentum complex in the teleparallel theory. In the Section

The metric tensor can be written in the tetrad form:

A general expression for an energy-momentum complex was found by Møller by using the method of infinitesimal transformations in the superpotential

The total energy is given by the surface integral below

In Einstein’s frame, Einstein-Hilbert-Maxwell action coupled with a string in four dimensions is given [

Taking

The general metric for this theory is written as

For the asymptotically flat black holes, the line element (

Taking

In this case the line element is [

In this case the line element is written by [

When we consider asymptotically non-flat black holes, the line element (

Now, the metric has the form [

At this point the metric becomes [

Here the metric becomes [

For this final case the metric becomes [

According to Lessner [

In the present work, in order to compute the energy distribution associated with some specific black holes in the Einstein-Maxwell-Dilaton Axion theory, we focus on the Møller energy-momentum distribution in the teleparallel gravity. For the asymptotically flat charged black holes, for all the cases (

The plot for the Möller energy versus radius, in the case of the asymptotically flat black holes.

Considering asymptotically non-flat charged black holes, for both the cases

These results agree well with the previous results [

This work is supported by the project DÜBAP-07-02-017.