{'fraction_non_alphanumeric': 0.03751803751803752, 'fraction_numerical': 0.011544011544011544, 'mean_word_length': 5.673076923076923, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Energy-momentum conservation in gravity theories.

We discuss general properties of the conservation law associated with a local symmetry. Using Noether's theorem and a generalized Belinfante symmetrization procedure in 3+1 dimensions, a symmetric energy-momentum (pseudo) tensor for the gravitational Einstein-Hilbert action is derived and discussed in detail. In 2+1 dimensions, expressions are obtained for energy and angular momentum arising in the ISO(2,1) gauge-theoretical formulation of Einstein gravity. In addition, an expression for energy in a gauge-theoretical formulation of the string-inspired (1+1)-dimensional gravity is derived and compared with the ADM definition of energy.