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Kind regards,

I just saw Christina's kind answer; one small correction though, I merely have a PhD and am not a professor by any means at this point in time ;-)

Kind regards,

So far, I did not receive any questions/comments by mail, something which is rather unexpected since generically, it seldomly happens that authors offer a public opportunity to provide comments about any work whatsoever. Concerning the response below, michael should define what it means to be ''nonlinearly stable''; assuming that the k_i are time functions and ''vacuum development'' is a Wick rotation, how would you define a Lorentz space in the context of general metric spaces and time functions ? For globally hyperbolic manifolds obtained by the usual Wick procedure from smooth time functions and smooth metric spaces, the answer obviously is yes since my notion of convergence does not hinge upon a chosen observer and hence, must be valid for all observers. Assuming, on the other hand, that ''vacuum development'' means solving the vacuum equations of motion, then I refer again to my first remark that he should define what it means in an observer independent context. I have never given this too much thought concerning gravity (as it is usually understood in some gauge) but there exist some pretty general results why, for the study of stability, it is sufficient to answer this question for the linearization of the field equations around some fixed point (that is, a static solution) and obviously, vacuum GR is not linearly stable in that sense (and therefore one would expect also nonlinearly stable, albeit some submanifolds of stable perturbations certainly can be found). However, I guess one would like to broaden the notion of stability to nonstatic solutions, in that case I am not even aware of any generally accepted definition of stability since there is no God given frame of reference. So, I do not understand why Micheal thinks that Sormani would find this aspect of my work unsatisfying given that nonlinear-stability does not even hold for more conventional notions of distance. Moreover, this stability of vacuum solutions is to my knowledge interesting for (a) a prelude to the massive case in which static solutions are totally unrealistic (b) to get a semiclassical grip on a would be ''quantum theory'' in case you would believe that the canonical quantization procedure applies to gravity. Concerning (a), all physical intuition tells one that this problem is unstable and (b) is in my opinion the wrong question to ask. I refer to http://www.vixra.org/abs/1106.0029 for further explanation why.

So far, I did not receive any questions/comments by mail, something which is rather unexpected since generically, it seldomly happens that authors offer a public opportunity to provide comments about any work whatsoever. Concerning the response below, michael should define what it means to be ''nonlinearly stable''; assuming that the k_i are time functions and ''vacuum development'' is a Wick rotation, how would you define a Lorentz space in the context of general metric spaces and time functions ? For globally hyperbolic manifolds obtained by the usual Wick procedure from smooth time functions and smooth metric spaces, the answer obviously is yes since my notion of convergence does not hinge upon a chosen observer and hence, must be valid for all observers. Assuming, on the other hand, that ''vacuum development'' means solving the vacuum equations of motion, then I refer again to my first remark that he should define what it means in an observer independent context. I have never given this too much thought concerning gravity (as it is usually understood in some gauge) but there exist some pretty general results why, for the study of stability, it is sufficient to answer this question for the linearization of the field equations around some fixed point (that is, a static solution) and obviously, vacuum GR is not linearly stable in that sense (and therefore one would expect also not nonlinearly stable, albeit some submanifolds of stable perturbations certainly can be found). However, I guess one would like to broaden the notion of stability to nonstatic solutions, in that case I am not even aware of any generally accepted definition of stability since there is no God given frame of reference. So, I do not understand why Micheal thinks that Sormani would find this aspect of my work unsatisfying given that nonlinear-stability does not even hold for more conventional notions of distance. Moreover, this stability of vacuum solutions is to my knowledge interesting for (a) a prelude to the massive case in which static solutions are totally unrealistic (b) to get a semiclassical grip on a would be ''quantum theory'' in case you would believe that the canonical quantization procedure applies to gravity. Concerning (a), all physical intuition tells one that this problem is unstable and (b) is in my opinion the wrong question to ask. I refer to http://www.vixra.org/abs/1106.0029 for further explanation why.

So far, I did not receive any questions/comments by mail, something which is rather unexpected since generically, it seldomly happens that authors offer a public opportunity to provide comments about any work whatsoever. Concerning the response below, michael should define what it means to be ''nonlinearly stable''; assuming that the k_i are time functions and ''vacuum development'' is a Wick rotation, how would you define a Lorentz space in the context of general metric spaces and time functions ? For globally hyperbolic manifolds obtained by the usual Wick procedure from smooth time functions and smooth metric spaces, the answer obviously is yes since my notion of convergence does not hinge upon a chosen observer and hence, must be valid for all observers. Assuming, on the other hand, that ''vacuum development'' means solving the vacuum equations of motion, then I refer again to my first remark that he should define what it means in an observer independent context. Moreover, as far as I know, the issue of nonlinear stability (as it is usually understood in some gauge) is also fully open in relativity (and obviously, vacuum GR is not linearly stable in that sense). So, I do not understand why Micheal thinks that Sormani would find this aspect of my work unsatisfying given that the answer is not even known for much easier notions of distance constructed in one particular gauge. Moreover, this stability of vacuum solutions is to my knowledge interesting for (a) a prelude to the massive case which is totally not understood (b) to get a semiclassical grip on a would be ''quantum theory'' in case you would believe that the canonical quantization procedure applies to gravity. Concerning (a), all physical intuition tells one that this problem is unstable and (b) is in my opinion the wrong question to ask. I refer to http://www.vixra.org/abs/1106.0029 for further explanation why.

So far, I did not receive any questions/comments by mail, something which is rather unexpected since generically, it seldomly happens that authors offer a public opportunity to provide comments about any work whatsoever. Concerning the response below, michael should define what it means to be ''nonlinearly stable''; assuming that the k_i are time functions and ''vacuum development'' is a Wick rotation, how would you define a Lorentz space in the context of general metric spaces and time functions ? For globally hyperbolic manifolds obtained by the usual Wick procedure from smooth time functions and smooth metric spaces, the answer obviously is yes since my notion of convergence does not hinge upon a chosen observer and hence, must be valid for all observers. Assuming, on the other hand, that ''vacuum development'' means solving the vacuum equations of motion, then I refer again to my first remark that he should define what it means in an observer independent context. I have never given this too much thought concerning gravity (as it is usually understood in some gauge) but there exist some pretty general results why, for the study of stability, it is sufficient to answer this question for the linearization of the field equations around some fixed point (that is, a static solution) and obviously, vacuum GR is not linearly stable in that sense (and therefore one would expect also nonlinearly stable, albeit some submanifolds of stable perturbations certainly can be found). However, I guess one would like to broaden the notion of stability to nonstatic solutions, in that case I am not even aware of any generally accepted definition of stability since there is no God given frame of reference. So, I do not understand why Micheal thinks that Sormani would find this aspect of my work unsatisfying given that nonlinear-stability does not even hold for more conventional notions of distance. Moreover, this stability of vacuum solutions is to my knowledge interesting for (a) a prelude to the massive case in which static solutions are totally unrealistic (b) to get a semiclassical grip on a would be ''quantum theory'' in case you would believe that the canonical quantization procedure applies to gravity. Concerning (a), all physical intuition tells one that this problem is unstable and (b) is in my opinion the wrong question to ask. I refer to http://www.vixra.org/abs/1106.0029 for further explanation why.