I read some papers about studies on metabolism in post-mortem tissues in human, but I do not exactly the reason about why our brain continues to have activity after death.
Your question is a little vague and as Christiaan mentioned, linking to the papers would be useful. If I understand, though, you want to know why cellular metabolic activity that takes places after someone dies?
If that's the case, the answer is essentially that whatever kills a complex organism in the sense of causing the heart to cease beating, doesn't immediately cause every cell in the body to stop functioning at the same moment.
Now for a slightly longer answer...Consider someone who suffers a heart attack and dies. Blood stops flowing through their veins and cessation of breathing means gas exchange stops. For cells with extremely sensitive oxygen and nutrient demands like cardiac cells, cell death begins to occur rapidly. Other cells farther down the blood and oxygen supply chain have a greater tolerance to disruptions in nutrient supply and would have at least some store of nutrients to work with after blood flow stops. Those cells will keep doing whatever they were doing for a little while; metabolizing nutrients, transporting metabolites, transcribing genes, etc.
After a while, though, even they will feel the lack of oxygen. At that point, most cells will switch over to anaerobic respiration. The eukaryotic fraction of cells in our body isn't particularly good at this, but can struggle on for a little bit until they simply run out of fuel and begin to die, largely through apoptosis.
Apoptosis of some cells will actually help prolong the lives of some of the cells neighboring the apoptotic ones, an effect that probably encouraged the evolution of apoptosis. After a while, though, too much apoptosis will have occurred and an uncontrolled sort death called necrosis will begin, leading to cascades of cell death and cessation of cellular metabolic activity. This process can take days to occur, depending on many variables surrounding the death of the organism.
So far, this has all been about eukaryotic cells; cardiocytes, adipocytes, myocytes, etc. These are the smallest fraction of cells in our body, by cell count. The rest of our bodies are composed of prokaryotic, or bacterial cells. This is our microbiome and this is where (for me) things get really interesting.
Although our microbiome exists in a symbiotic relationship with our eukaryotic cell fraction, many members of the microbiome are less dependent on the nutrients found in our blood system than those eukaryotic cells. The cells of our microbiome are also frequently much more capable of surviving in low-oxygen or even anaerobic environments. These parts of us will continue to thrive for some time after we "die".
Some of our microbial cells, if left to their own devices, could even find new environmental niches outside our bodies and continue to live long after "we" have died. The quotes around 'die' and 'we' become necessary at this point because from here, questions of identity and life branch into the philosophical.
This became a lengthy answer, but I find it a really interesting topic. Here's a nice article from the Guardian, that discusses post-mortem cellular metabolism and our microbiomes in particular: https://www.theguardian.com/science/neurophilosophy/2015/may/05/life-after-death
To elaborate on the comments - I think the question hinges on the definition of 'death'.
A brain-dead person is considered clinically dead. However, vital functions such as respiration and blood flow can be maintained artificially and pretty much indefinitely. So under active ventilation, a person in a brain-dead state feels warm to the touch and seems to be breathing normally. Yet, the person is dead (source: WebMD).
So as to your question I dare say that after death, there is no neural activity.
Conversely, when there is still brain activity I do not think the person is declared clinically dead. For example, cardiac and respiratory arrest can be acted upon by resuscitating the person. If the brain of such a person ceases to show activity, then little chance such a person will survive.
- Goilar & Pawar, Indian J Crit Care Med; 13(1)
PS: I edited the tag wiki to define human death more strictly